Sandy Ingram, 80, had been searching in his garden for two intruders he had seen late at night and was later discovered lying motionless.
He underwent brain surgery after the incident on June 19, 2010 outside his Newmachar home in Aberdeenshire. Mr Ingram spent time in a high-dependency unit in Aberdeen Royal Infirmary but never recovered and died a year later.
Four years on, police are no closer to solving the case and Sandy's family are appealing for anyone with answers.
His son Andrew said the family believed that someone was responsible.
He said: "It has been such a long time now - we just want answers and to find out what happened.
"You would think that someone would have a guilty conscience and that they might speak about it."
Andrew urged anyone with any information to come forward. He added: "Even if you think the information is not relevant and even if you think it won't help, please come forward and tell us. It just might help."
Detective Inspector Richie Guild, who has overseen the investigation, said: "Anyone who may have information as to what happened to Mr Ingram is urged to contact Police Scotland."